Watch a pond closely and you'll likely see hundreds of little water striders zipping across the water with remarkably long, thin feet. What determines the precise length of the bugs' feet? A new calculation suggests that evolution has optimized their length: They're just long enough to support the maximum possible weight without adding needless drag.
Striders rely on surface tension to keep themselves afloat. Water molecules attract one another, pulling the surface taut like a drumhead so that it can support the weight of an object even if the object is denser than the water itself. Of course, the object has to be light and wide to spread its weight out across the surface. That's why the water strider's feet are so long. Since Galileo, scientists have studied such phenomena, and physicists have analyzed simple models of objects like water striders' feet such as finitely long rods or finite but inflexible rods floating on surfaces. But all these calculations have left a simple question unanswered: What determines exactly how long a water strider's feet should be?
Dominic Vella, a physicist at the École Normale Supérieure in Paris, decided to find out. To do so, he added a simple but key twist to the calculations: He modeled the foot as a rod of finite length that, like real water-strider feet, could bend like spring steel. That little bit of bending changes everything. Push down on a rigid rod, and the whole thing pushes into the water. So the total upward force equals the force of surface tension times the rod's length, and the amount of weight the rod can support simply increases with its length.
That's not so for a flexible rod. Think of a child in a pool bobbing on a long, thin foam float called a pool noodle, which is held up by buoyancy and not surface tension. As the child moves to one end, that side of the float dips a bit below the water and the opposite side bends up out of the water. The upward force on the float gets progressively smaller farther away from the child. The force on the noodle drops to nothing for the end that's out of the water, as the water can't support something that's not touching. Much the same thing happens for a bendable rod supported by surface tension, Vella says.
Vella developed an equation to determine how much surface tension supports a bent leg of any given length could achieve. At very short lengths, the leg is essentially rigid, so adding more length increases the amount of weight it can support. But at a certain point--which depends on the radius of the leg's curvature and its elasticity--adding more length makes the object bend significantly. That adds drag but doesn't increase the weight the thing can support. Vella then measured water strider legs and found they were just shorter than this critical length, he reported this month in Langmuir. "Evolution's testing that limit out," he says.
Other scientists have hypothesized that bending would affect the upward force, but Vella's equation shows exactly how to optimize the load for a bent object of various lengths and materials, says Metin Sitti, a mechanical engineer at Carnegie Mellon University in Pittsburgh, Pennsylvania. Sitti says his team has already built robots of varying sizes that use surface tension to walk on water, but knowing the detailed math behind the physics will be useful.